UNIT I: CONCEPT ENHANCER- NEWTON’S 2ND LAW
In the exploration activity Spring Skaters, you explored the relationships between force, mass and acceleration in order to develop Newton’s 2nd Law. In these activities you discovered the variables that affected acceleration. We call acceleration the dependent variable because it depends on the value of other variables such as force and mass. Force and mass are independent variables because we can change them by manipulating their values. In this activitywhen you pulled hard enough, the cart changed velocity. It accelerated. When you pulled still harder the cart accelerated again, but the rate at which the speed changed was increased (you got to a high velocity faster) or you could say you had a greater acceleration. You knew this by the way your feet had to move faster and faster so that you could keep the force constant. So force is directly related to acceleration. You also found that if you pulled on a more massive person that the acceleration was less. So acceleration is inversely related to mass. This can be summarized as
a = F/m,
which is a form of Newton’s 2nd law of motion. The force in this equation is actually the net force acting on an object, which means that you have to add up all the forces on the object that you are trying to accelerate. This relationship is often solved algebraically for force and written as
Fnet = ma
This might appear to be a simple law but it has dynamic implications. In Can You Change Your Motion when you began the experiment you had a small mass on the end of the string, which resulted in a force of tension acting on the cart. The cart (and the hanging mass) accelerated according to Newton’s 2nd law. As you added more mass to the string you increased the force due to the weight of the hanging mass which acts on the system of the cart and the hanging mass. The mass of the cart remained constant so the acceleration of the system increased.
Fnet = ma
And as you added still more mass on the end of the string (and thus more force as weight on the end of the string), the acceleration got even larger.
Fnet = ma
This is what is meant by a direct relationship. If you doubled something on one side of the equation, the other side also doubles. Triple one side – the other side also triples. Reduce one side by one half reduces the other side by one half.
When you started adding more mass to the cart but keeping the force on the string (the weight of the hanging mass) the same, the acceleration reduced. Therefore mass and acceleration are inversely proportional. If one quantity goes up and the other goes down, the product can remain the same as in the case of mass and acceleration
Fnet = ma
Now lets look at net force again. Did all the force with which you pulled produce acceleration of the cart or skater? When you pulled on the cart you applied a force. If you pulled harder the cart would begin to move but at a steady or constant speed. A constant speed means the acceleration is zero. Doesn’t this violate Newton’s law? Aren’t you supposed to be accelerating? Zero acceleration means that the net force is zero, which means the sum of all forces on the cart is zero and therefore, any forward force has to be balanced with a retarding or negative force. This negative force is known as friction (Ffriction) which opposes or acts in the opposite direction to motion. By definition
Fnet = Ffriction + Fapplied
Be careful how you handle the signs. When you substitute a value for friction, it will be negative and therefore the net force will be the difference of the applied force and friction. The net force could also be called the accelerating force since it is the amount of force left over to accelerate you after you subtract friction off your applied (or pulling) force. So not all of the spring scale force (pulling or applied force) goes in to the acceleration. There will only be one unique value of the applied force that will cause zero acceleration and that is when the value is equal to friction.
Lets take another example – a rock falling downward. When the rock begins to fall it accelerates. Initially the only force acting on the rock is gravity or the gravitational attraction between the rock and Earth. This force of gravity on the Earth is defined as weight. So when you measure your weight, you are measuring the Earth’s attraction for you.
As the rock speeds up air resistance becomes significant. Think about going for a ride in a slow moving car with your arm out the window what do you feel? Air friction. What happens to that air friction as you go faster and faster? It gets larger and larger. The same thing happens to the rock. For a falling object, the force of air friction pushes the object upward and the force of gravity pulls it downward. You can define up or down positive as you wish, but the forces will be in the opposite direction and when values are substituted into the equation you will be taking the difference in the two values to calculate the net force.
Fnet = Fweight + Ffriction = ma
As friction increases the net force decreases and therefore the acceleration decreases. Notice that the force of gravity doesn’t change but yet the rock has a lower acceleration and the net force (accelerating force) is also smaller.
What happens if the frictional force equals the force of gravity? Wouldn’t the net force become zero as well as the acceleration?
0= Fweight + Ffriction = 0
So with no net force there is no acceleration. This is defined as terminal velocity. The rock still has forces acting on it but the forces are equal and opposite so there is no more speeding up (acceleration) for that rock but the rock is still moving. The average skydivers terminal velocity equals 63 m/s (227 km/hr or 141 mi/hr) downward before the parachute is opened. Once they open their parachute, their average terminal velocity is around 3 - 4 m/s (7 - 9mi/hr) downward
Is there a difference between mass and weight? Weight is a force and can be calculated using Newton’s 2nd law
Fweight = ma = magravity
wherea is the acceleration due to gravity (g).
If John’s mass is 60. kg what would he weigh?
Fweight = (60. kg)(9.8 m/s2) = 590 but what is the unit?
The unit for weight and for all forces is a Newton (N) so John would weigh 590 N. Since 4.4 N = 1 lb, John’s weight in pounds would be about 134 lbs. Since force is a vector quantity, direction must also be included. Since the acceleration of gravity is directed downward, John’s weight would also be directed downward. As a result, the force of gravity (or weight) acting on John would be 590 N or 134 lbs directed downward.
Name ______Period ______
UNIT I: CONCEPTUAL PRACTICE – NEWTON’S 2ND LAW
1. Galaxy weight loss had a great offer – lose 5/6 of your weight in two days. All you need do is travel to and live on the moon where gravity is 1/6 that of the Earth. What is wrong with this idea?
2. If an object is not accelerating, can you conclude that no forces are acting on it? Explain.
3. If we say that one quantity is proportional to another quantity does this also mean they are equal to each other. Explain using mass and weight in your example.
4. With your knowledge of Newton’s 2nd law sketch graphs for the following scenarios:
- John is comparing the force on his bicycle pedal with acceleration while his mass remains constant (Figure 1.8.1).
Figure 1.8.1
- What is the likely relationship between the number of cars and mass of a train and its acceleration if the force delivered by the engine remains constant (Figure 1.8.2)?
Figure 1.8.2
c.Heather compares the weights of laboratory masses (Figure 1.8.3).
Figure 1.8.3
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